Bases Raised To Even And Odd Exponents

What happens when we raise a negative exponent to an odd number? Eg: (-x)³

• The result will be negative

• The result will be either positive or negative depending on the value of x

• The result will be positive

• The result will be an imaginary number.

Evaluate the following based on the rules of exponents:

-2²

(a)  

Answer explanation

There are no brackets around the -2, so the square only squares the two, not the negative symbol.

Evaluate the following: (-3²)

(a)  

Evaluate the following: -(2 x 3)³

(a)  

Jenny sees the following in a test. 2 x (-5)². She says that you calculate the answer by doing the following:

(2² x 5²) / -1. She is incorrect. What has she done incorrectly? Select all that apply.

• She multiplied the two terms

• She divided her result of the two terms by -1

• The calculated 2² when there was no squared sign

• She forgot the negative before the 5

Evaluate -- without a calculator: ((-6)³ + 2³ x -5)

(a)  

I have a number. It is negative. I raise it to the power 4 and subtract 3. Take x as the number. Answer the following questions:

Write an expression for the sum above.

• 4 + 3x

• (-x)⁴ - 4³

• (-x)⁴ - 3

• -x⁴ - 3

I have a number. It is negative. I raise it to the power 4 and subtract 3. Take x as the number. Answer the following questions:

Will the answer be positive or negative? Why?

• Positive because you have multiplied a negative number by itself an even number of times times.

• Negative, because you have multiplied a negative number by itself an even number if times

• It could be either depending on the value of x because you subtract 3

• It is neither positive nor negative unless x is even.

I have a number. It is negative. I raise it to the power 4 and subtract 3. Take x as the number. Answer the following questions:

Take x as -4. Evaluate your expression.

(a)  

I get an answer of -5 after evaluating an expression. Which expression below may I have evaluated?

• 6x - 3

• (-3x + 6) x 2

• (-6x) / 5

• (-6x) / 3 + 1